Special equipment: four 4-ounce ice-pop molds or six 3-ounce molds, 4 or 6 ice-pop sticks,Prepare a grill or large grill pan for high heat.,Bring the ginger, sugar and 1/4 cup water to a simmer in a small saucepan.,Cook on medium-low for 10 minutes.,Let cool completely at room temperature, at least 30 minutes.,Meanwhile, brush the peach halves all over with the butter.,Place them cut-side down on the grill, and grill until very charred, about 5 minutes.,Flip the peaches, and grill until the rounded side is charred in spots and the peaches are tender but not falling apart, about 5 minutes.,Transfer to a plate to cool completely, about 20 minutes.,Put the cooled peaches, preserves, 1/2 cup of the almond milk, lemon juice and a small pinch of salt in a blender.,Strain the cooled ginger syrup into the blender, pressing the ginger pieces in the strainer with the back of a spoon to extract as much flavor as possible; discard the ginger.,Puree the peach mixture until completely smooth, scraping down the sides of the blender partway through if needed.,Transfer the mixture to a large liquid measuring cup with a pouring spout.,Pour the mixture into the ice-pop molds, leaving 1/4 inch of space at the top (the mixture will expand).,______,Freeze until solid, 5 hours to overnight.,When ready to serve, put the remaining 1/2 cup almond milk in one drinking glass and the almonds in another.,Unmold the ice pops, and dip the top of each into the almond milk, then into the almonds.,Serve immediately.